Non-dominated sorting genetic algorithm-II for possibilistic mean-semiabsolute deviation-Yager entropy portfolio model with complex real-world constraints

Abstract

The purpose of our paper is to address the multi-objective portfolio model with complex real-world constraints under the assumption that the returns of risky assets are fuzzy variables. Firstly, a new possibilistic mean-semiabsolute deviation-Yager entropy portfolio model is proposed with transaction costs, cardinality and quantity constraints Secondly, to solve the proposed model efficiently, a non-dominated sorting genetic algorithm-II (NSGA-II) is presented, which can not only reduce the computational complexity but also enhance the solution accuracy. Then, a numerical example is provided to verify the feasibility and effectiveness of our proposed model and algorithm. Based on these results, we analyze the efficient frontiers with different quantity constraints and transaction costs, and illustrate the portfolio distributions with different transaction costs by using the boxplot figures. Finally, these solutions solved by NSGA-II and four traditional computation methods are compared. Our proposed algorithm outperforms the minimax method (Polakabb, 2010), two-stage method (Masson, 2016), extended two-stage method (Li, 2012) and compromise approach-based genetic algorithm (Li, 2013) in the efficient frontier, accuracy and number of solutions.